Can this software be used to design a logo?
yes indeed, In fact, Blender does more than I really expected to get from a free software.
Blender can be used to: Model in 3D, UV map, Texture, Rig for animation, Animate in 2D and 3D, even make games using the logic brick method. So yes, a logo is a simple matter for a user of Blender.

But naturally, it will take time and a bit of practice to get good, but hey, when you're there, you're there.